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In a certain region of space, there exists a uniform and constant electric field of strength \( E \) along \( x \)-axis and uniform constant magnetic field of induction \( B \) along \( z \)-axis. A charged particle having charge \( q \) and mass \( m \) is projected with speed \( v \) parallel to \( x \)-axis from a point \( (a, b, 0) \). When the particle reaches a point \( \left(2 a, \frac{b}{2}, 0\right) \) its speed becomes \( 2 v \). Find the value of electric field strength.
(A) \( \frac{3}{2} \frac{m v^{2}}{q a} \)
(B) \( \frac{m v^{2}}{q B} \)
(C) \( \frac{2 m v^{2}}{q B a} \)
(D) \( \frac{3}{2} v B \)
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